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In a study of the effects of exposure to lead on the psychological and neurological well-being of children, a group of children who lived near a lead smelter in El Paso, Texas, were identified and their blood levels of lead were measured. An exposed group of 19 children were identified who had blood-lead levels of at least 40 mg/ml. This group of children is defined by group variable leadtype and was coded as 2. A control group of 63 children were also identified who had blood-lead levels less than 40 mg/ml, and is identified by the variable leadtype and was coded as 1. All children lived close to the lead smelter. Two important outcome variables were (1) the number of finger-wrist taps in the dominant hand (a measure of neurological function) and (2) the Wechsler full-scale IQ score. The data is saved in text (or ascii) format leadtest.dat, EXCEL format leadtest.xls and SPSS format leadtest.sav. They can all be downloaded from WebCT Course Material page.
Variable DescriptionidIdentification numberareaArea where the children lived 1 = 0 to 1 mile from smelter 2 = 1 to 2.5 miles from smelter 3 = 2.5 to 4.1 miles from smelterageAge, 1011 mean 10 years 11 monthssexSex 1=Male, 2=FemaleiqfFull Scale of IQ test scoreleadtypeBlood lead level group 1 = below 40 mg/ml 2 = greater or equal to 40 mg/mlfwt_rFinger-wrist tapping test right handfwt_lFinger-wrist tapping test left handmaxfwtLarger of fwt_r and fwt_l as a proxy for the number of taps from the dominant hand
Perform the analyses indicated below. In each case, be sure to provide a written description of the results using plain language. You may use any statistical or spreadsheet software you wish (cut and paste the graphs into this file), or you may do the work by hand.
Identify the type (qualitative or quantitative) of variable measured except for id.
Are the children with higher blood-lead levels likely to have lower IQ score? Illustrate with a graph and numerical summaries.
Describe the shape of the distribution of IQ scores for children from each leadtype group with graphs.
Are the children with higher blood-lead levels likely to have lower number of taps in finger-wrist tapping test from the dominant hand? Illustrate with a graph and numerical summaries.
Describe the shape of the distribution of numbers of taps in finger-wrist tapping test from the dominant hand for children from each leadtype group with graphs.
If we assume that the IQ test scores are normally distributed, find the 95% confidence interval estimate for the average IQ scores for the population of the children considered in this study.
Assume that the IQ scores are normally distributed for children from each of the two subgroups that had different blood-lead level. Find the 95% confidence interval estimates for the IQ scores for the group of children whose blood-lead level below 40 mg/ml.
Do we really need the normality assumption to do problem 7)? Can we do it without the normality assumption? Explain.
Assume that the data represents a random sample of children from the population. At the level of significance 0.05, test whether the average IQ scores for the population of children who had high blood-lead level (leadtype = 2) considered in this study is different from 90. State the null and the alternative hypotheses, find the p-value and draw a conclusion.
Use the data to test whether there is a significant different in average IQ between children who had high blood-lead and those who dont have high blood-lead. Test the hypothesis at the level of significance of .05. Also, find the 95% confidence interval estimate for the difference of the means IQs of the two groups of children.
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